verify : [sec(x) / csc(x) - cot(x)] - [sec(x) / csc(x) + cot(x)] = 2csc(x)
Use the following identities to express everything in sin(x), cos(x), tan(x) and cot(x):
sec(x)=1/cos(x)
csc(x)=1/sin(x)
Unless there is a typo on the right-hand-side, I find the given identity not true.
i put it in my graphing calculator, though, and they graph the same function
This is why I suspected there is a typo.
The left-hand-side evaluates to -2csc(x).
The right-hand-side, 2*csc(x).
I suggest you recheck the expressions posted.
Here's a plot of each side of the identity as posted.
http://img508.imageshack.us/img508/3851/1294005524.png
The left-hand-side evaluates to -2cot(x).
To verify the given equation:
[sec(x) / csc(x) - cot(x)] - [sec(x) / csc(x) + cot(x)] = 2csc(x)
We need to simplify both sides of the equation and check if they are equal.
Let's start with the left side:
[sec(x) / csc(x) - cot(x)] - [sec(x) / csc(x) + cot(x)]
To simplify this expression, we need to find a common denominator for the denominators of the fractions involved. In this case, the common denominator is csc(x).
The first term can be written as (sec(x) * csc(x)) / csc(x) = sec(x)
The second term can be written as (cot(x) * csc(x)) / csc(x) = cot(x)
Now let's substitute these into the original expression:
sec(x) - cot(x) - sec(x) - cot(x)
We can combine like terms:
(sec(x) - sec(x)) + (-cot(x) - cot(x)) = -2cot(x)
Now, let's simplify the right side of the equation:
2csc(x)
We can't directly combine these two sides since they are not equal.
Therefore, the given equation is not verified.